The literal significance of the scene is, as the writer above points out, the decision that Brutus makes to betray and murder Caesar. The scene also has symbolic significance if you consider the setting. Brutus makes the decision in his garden at 3 a.m. (the devil's hour) when he decides that Caesar must be killed before he could do more harm. In making this decision, Brutus compares Caesar to a serpent still in the egg: “And therefore think him as a serpent’s egg, / Which, hatched, would, as his kind, grow mischievous, / And kill him in the shell.” (33–35) The garden, the hour, and the serpent all suggest the fall of man in the Garden of Eden. Here Brutus is making the conscious decision to sin by betraying his friend and emperor. The murder itself has been compared by critics to the betrayal of Abel by his brother Cain.
This scene is important because Brutus finally makes the decision to kill Caesar. After this scene, there is no going back. He becomes the leader of the conspirators, replacing Cassius. Brutus is doing this for Rome since he considers Caesar to be a threat to the future of Rome. He refuses to allow Antony to be killed since he feels this would be wrong, a decision that he will later regret.